Application of k-Laplace transform to estimate the time value of money in quantitative finance


V. R. Lakshmi Gorty


In this study, the fractional Laplace transforms is shown to be more useful to deduce existing value rules. Not many analytic solutions exist for present value problems; with k-Laplace transforms, some of the closed form solutions are efficient. The boundary of the integral is from 0 to some finite quantity. When the change takes the upper bound to infinity, then the present value of a future cash flow is the-Laplace transform of the current cash flow.

Literature review of continuous finance

The author (David, 2001) states that when an entity uses the interest method, the statement requires a careful description of: the cash flows to be used (promised cash flows, expected cash flows or some other estimate), the convention governing the choice of an interest method (effective rate or some other rate), how the rate is applied (constant effective rate or a series of annual rates) and how the entity will report changes in the amount or timing of estimated cash flows. Agnė Pivorienė, (2017) analysed the valuation of financial instruments; project valuation techniques usually assume that expected cash flows are discounted at discrete intervals, e.g., daily, monthly, quarterly, semi-annually, or annually. In some instances, especially for high-risk investments, continuous discounting can be used for more precise valuation. The author also mentioned an example of the technique of continuous discounting which is widely used in financial options valuation and primarily in the Black-Scholes option pricing model. In another study, a discrete-continuous project scheduling problem with discounted cash flows was considered. In discrete-continuous project scheduling, activities required for processing discrete and continuous resources were also analysed. The processing rate of an activity is the same function of the amount of the continuous resource allotted to this activity at a time (Grzegorz Waligóra, 2015).

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